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Low-rank tensor reconstruction of concentrated densities with application to Bayesian inversion
Martin Eigel, Robert Gruhlke, Manuel Marschall
Transport maps have become a popular mechanic to express complicated probability densities using sample propagation through an optimized push-forward. Beside their broad applicabil…
An adaptive stochastic Galerkin tensor train discretization for randomly perturbed domains
Martin Eigel, Manuel Marschall, Michael Multerer
A linear PDE problem for randomly perturbed domains is considered in an adaptive Galerkin framework. The perturbation of the domain's boundary is described by a vector valued rando…
Adaptive stochastic Galerkin FEM for lognormal coefficients in hierarchical tensor representations
Martin Eigel, Manuel Marschall, Max Pfeffer +1
Stochastic Galerkin methods for non-affine coefficient representations are known to cause major difficulties from theoretical and numerical points of view. In this work, an adaptiv…